I don't think your using it enough. If you fill it all the way and it takes months to use it, then yes, it probably will stink. Try draining it and sanitizing it with bleach. I put a couple of good glugs (careful measurement is crucial) in it then fill. Run all faucets still you smell the bleach and let it sit overnight. Drain and refill and run all the faucets until odor is gone.
If you don't want to use it a lot, just put a few gallons of water in so you will have to add fresh water often. I do this twice a year. We cook and make coffee with it. We don't usually drink it straight from the tap because of the tastes from different parts of the country. Haven't gotten sick yet.